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Even though she got a 22 on her ACT math, D just failed a placement test because they wouldn't allow calculators. Doing math in your head or on scratch paper is ideal, but is it really expected of students in this day and age? Failing the placement test means she has to take a remedial math class.

That's unfortunate, but not uncommon. Even though calculators are the norm and are used in math classes, the placement tests are usually to test for both basic skill set and speed at calculations. Plus, if they allowed calculators, the upper level math classes would be bursting, as most students can do math both fairly accurately and quickly with a calculator (not to mention if they have graphing calculators they can store formulas on them to assist with the placement exam). It's too bad it didn't work out for your D, I'm sure she's a very good math student, but maybe taking remedial math will be good for her, as it will allow her to brush up on her skills without stressing too much.

She may be disappointed to have to take the remedial class, but it would have been much worse to land in a college math class she is unprepared to take. This may end up helping her in the long run.

> Doing math in your head or on scratch paper is ideal, but is it really expected of
> students in this day and age?

I think that it should be.

When I read a news story or a financial report or a research paper, I mentally make calculations in the background as to whether the numbers are reasonable as people that write news articles make errors in calculations. When someone tells you something that seems unreasonable, do you go through the calculations in your head? If your calculator gives you an answer, do you verify that the answer is reasonable?

A 22 is about a median score on a test that is set far below the level of most college math. It doesn't surprise me much that someone whose ACT math score was a 22 would wind up in a remedial college math class, and it probably has little or nothing to do with calculators vs. pencil-and-scratch-pad. Her command of basic high-school math is probably less than complete.

And why would her parents object? One way or another, you are paying in sweat and treasure for her to get a college education. Don't you want to defer to the judgment of the professionals about what she has to do to get the most out of college? Wouldn't you prefer that she actually learn fundamental math solidly once and for all than that she struggle in a class where doing well may be beyond her knowledge base?

When S2 (not a good math student) took the math placement test at orientation, the instructions sent to him in the mail prior to the test date said calculators were allowed but only basic ones, no scientific graphing calculators. Since all he had was a graphing calc., I went to Target and bought the most basic $5.99 calculator. He did not pass the test but what really annoyed him was that he saw others taking the test using the sophisitcated calculators even though the letter had said they would not be allowed.
S2 said he could have done much better if he had also had a better calculator.

In S2's case, it didn't really matter since at his school, there is only one math required for humanity/non-techy majors (which he is) and it doesn't not require a certain score level on the placment test. The only reason he had to take the test was to have a score available if he decided at some point to change majors to one that required more math.

I was not a good math student either and had to take remedial math as a freshman.
It really wasn't that bad and helped me a lot (poor h.s. math background) in the long run since I was a nursing major.

Actually, it looks like the median ACT math score is 20. But take a look at this: [url] http://www.act.org/standard/pdf/CRS.pdf[/url]. A 22 ACT score indicates meaningfully less facility with math than I hope my English-teacher kid has.

I don't see what difference being at a state school makes, and it's obvious she isn't a math major, and probably won't ever be one. The kind of responsible job you hope your college-graduate daughter gets requires a level of basic mathematical problem-solving ability that she may not have command over yet. If you want her college degree to represent a real certification of knowledge and competence, you want her to take the math they think she needs to take.

Having taught remedial college math many times, I would observe that very few of those students are placed there by mistake. She may feel better about it by blaming the lack of a calculator, but few if any of the problems are of the sort: multiply 389 X 53887 or Add this giant column of numbers, etc.

After your D takes the remedial class, which math course(s) will she be taking to fulfill her math requirements?

An example she mentioned from the test was the square root of 95. I don't know what her choices were so I can't comment on how difficult that would be to solve.

As an early childhood ed. major, she needs to take Calc I (4 credits) OR Intro to Statistics (3 credits) AND Discrete Probability (3 credits). So if she wants to avoid calculus, it means taking a third math class.

I don't know what the format of the test was but assuming that there were five answers, I'd guess that three were bogus and two were close. The square root of 100 is 10 and the square root of 81 is 9. The difference is almost 20 so 5 from the top would be about a quarter down. A quarter down from 10 is 9 3/4 or 9.75. So that should eliminate three answers. She could just then square the remaining two answers to see which comes closest. That's trivial to do on a four-function calculator.

I just looked up the actual square root and it is 9.7467, pretty darn close to the estimate above.

Worst case if the above approach with ratios wasn't known: just square all five answers on the four-function calculator and see which comes closest.

D, now a college seniorA) went to a progressive K-8 school that didn't have a good math program and never learned basic arithmetic thoroughly (didn't have to memorize times tables, barely spent time on long division, and the like). In high school she was always allowed/encouraged to use a calculator; she aced every math course including AP stat and calculus; and got 710 on the SAT math with no special prep--all using a calculator. She took a few math/math application courses in college, using calculators or computer program, and did well. NOW she is planning to take the GRE in mid-January. NO calculator is allowed...and she's panicking with some reason. She can't remember long division or even how to "borrow" in subtraction. She'll probably have to use much of her prep time during winter break to learn/relearn all of this.

Since H and I are both statisticians and know she has a good head for math, we are chagrined about this...

Hey, BCEagle, anyone who's been reading this forum for any length of time knows you're a whiz with numbers. You'd pass with flying colors. (BTW, I always love reading your posts when it comes to finances.)

I agree with BCEagle that calculators should not be permitted on math placement tests. College students should be able to do arithmetic with pencil and paper! Also doing quick estimates in your head is a very useful skill in this increasingly quantitative and technical world. Calculators do have their place, but over-reliance on them leads to sloppy quantitative thinking.

I have a K-8 set of standard math textbooks from the early 1990s at home. I'm pretty sure that the above square root stuff is covered somewhere between grades 5-7 in those textbooks. Those textbooks had technology sections for calculators but they also encouraged mental math and estimation.

I was pretty disappointed with the changes in math texts in the late 1990s - I call it the rainforest math approach. I think that there are benefits from traditional math and newer approaches and that school districts should try to use the best from both approaches. That doesn't necessarily sell textbooks though. In my school district, two out of three elementary schools supplement the state-standards textbooks with traditional math (the standards were written such that one textbook publisher basically has a lock on textbook sales). This is done by the teachers voluntarily as it isn't in the state standards nor in the district requirements. The other school doesn't. Guess which schools parents complain about.

I think the problem is less the lack of calculators on the placement tests and more the overuse of them in school prior to this. H says that kids in his HS bio classes have no concept of what numbers mean--answers just come out of the void on their calculators. And if the calculator says it; it's right. So, if they divide 10 by 100, for instance, but put in the numbers wrong, and get 10 as the answer, they won't see it doesn't make sense--the calculator says it so it must be right. He'd ban all calculator use before middle school, maybe high school, so they'd acquire basic number sense (the kind BCeagle demonstrated above.)

Doing math in your head or on scratch paper is ideal, but is it really expected of students in this day and age?

It is in my math class. Even in classes for which I expect students to use calculators heavily, I expect them not to use calculators for basic computation. It's pointless to make students multiply two four-digit numbers by hand if they can already do it, or divide 3.51*10^5 by 4.3*10^(-9) manually if they can already do it, but if they can't already do it, they haven't achieved a basic level of math proficiency that we expect of high school graduates. And I certainly expect that my students will not reach for a calculator to multiply 17 by 5, or approximate pi/2, let alone the square root of 95.

Calculators are fabulous labor-saving tools. But a student who can't do arithmetic or basic algebra without one really does need remedial math. If her high school graduated her without these skills, it did her a disservice. But I don't think that means her college should just pass her along that way.

In your situation, I'd be annoyed and disappointed and frustrated, too. But I don't think the college is really the right entity for you to be ticked off at.

Hey, BCEagle, anyone who's been reading this forum for any length of time knows you're a whiz with numbers. You'd pass with flying colors. (BTW, I always love reading your posts when it comes to finances.)

No one would ever mistake me for a math wiz and I used the same concept as BC. I knew that 9*9 =81 and 10*10 =100 since 100-95 =5, I would have also chosen the largest number over 9 and under 10.

My daughter also went to a school that did Marily Burns Math for smarty pants and knew how to do all sorts of abstract word problems but struggled doing basic arithmetic in her head. Yes, I whipped out my index cards and that is how she learned multiplication.

I agree with Garland about the over reliance on calculators. Kids with high tech calculators simply program formulas in their calculators and then plug and chug without really knowing how to do the work pen to the paper.

> In your situation, I'd be annoyed and disappointed and frustrated, too. But I don't
> think the college is really the right entity for you to be ticked off at.

Schools have 12 years to teach at least arithmetic and algebra. That is a very, very long time. If the schools aren't doing their jobs, then parents have to step in to fill the void. The problem is that parents often don't know that there is a problem.

I recall the survey results in grad school on how to improve courses. The biggest complaint was on students that didn't have the prerequisites for the course eating up valuable course time. How can a college professor teach the required material if a lot of course time is spent doing prerequisites?

In this case, the placement tests are fair to everyone. The professor can teach the course. Students in the course aren't held back by students that won't succeed in the course. Students that have to take remedial courses will be prepared for the course after they can demonstrate that they can meet the prerequisites.

It all depends on what the purpose of the exam is, and the level of student we are talking about. One should certainly be able to estimate, but if they require you to estimate they should make sure it is appropriately easy to discern between the answer choices using estimation.

At some level, the test should be designed to evaluate knowledge of the math concepts, not entirely the ability to perform arithmetic and estimation.

For example, I think it would be far more effective use of time to have several questions along the line of "What is ln(e^6.37)", rather than questions like "Estimate the number closest to e^6.37". In the case of the latter question, depending on the answer choices given, you would merely have to narrow it down and guess.

He'd ban all calculator use before middle school, maybe high school, so they'd acquire basic number sense...

Right on! Students need "basic number sense" to know if the numbers their calculators produce are reasonable. In most college science courses, plug-and-chug leads to poor understanding. The successful students are the ones who have an approximate idea of what the solution should be before they start entering numbers in a calculator.

## Replies to: Math Placement Test Without a Calculator?

> students in this day and age?

I think that it should be.

When I read a news story or a financial report or a research paper, I mentally make calculations in the background as to whether the numbers are reasonable as people that write news articles make errors in calculations. When someone tells you something that seems unreasonable, do you go through the calculations in your head? If your calculator gives you an answer, do you verify that the answer is reasonable?

And why would her parents object? One way or another, you are paying in sweat and treasure for her to get a college education. Don't you want to defer to the judgment of the professionals about what she has to do to get the most out of college? Wouldn't you prefer that she actually learn fundamental math solidly once and for all than that she struggle in a class where doing well may be beyond her knowledge base?

S2 said he could have done much better if he had also had a better calculator.

In S2's case, it didn't really matter since at his school, there is only one math required for humanity/non-techy majors (which he is) and it doesn't not require a certain score level on the placment test. The only reason he had to take the test was to have a score available if he decided at some point to change majors to one that required more math.

I was not a good math student either and had to take remedial math as a freshman.

It really wasn't that bad and helped me a lot (poor h.s. math background) in the long run since I was a nursing major.

The average ACT math score in the US is a 21. Also, this is a state school, and D isn't a math major. We didn't plan on an extra class.

I don't see what difference being at a state school makes, and it's obvious she isn't a math major, and probably won't ever be one. The kind of responsible job you hope your college-graduate daughter gets requires a level of basic mathematical problem-solving ability that she may not have command over yet. If you want her college degree to represent a real certification of knowledge and competence, you want her to take the math they think she needs to take.

After your D takes the remedial class, which math course(s) will she be taking to fulfill her math requirements?

As an early childhood ed. major, she needs to take Calc I (4 credits) OR Intro to Statistics (3 credits) AND Discrete Probability (3 credits). So if she wants to avoid calculus, it means taking a third math class.

I just looked up the actual square root and it is 9.7467, pretty darn close to the estimate above.

Worst case if the above approach with ratios wasn't known: just square all five answers on the four-function calculator and see which comes closest.

Since H and I are both statisticians and know she has a good head for math, we are chagrined about this...

I was pretty disappointed with the changes in math texts in the late 1990s - I call it the rainforest math approach. I think that there are benefits from traditional math and newer approaches and that school districts should try to use the best from both approaches. That doesn't necessarily sell textbooks though. In my school district, two out of three elementary schools supplement the state-standards textbooks with traditional math (the standards were written such that one textbook publisher basically has a lock on textbook sales). This is done by the teachers voluntarily as it isn't in the state standards nor in the district requirements. The other school doesn't. Guess which schools parents complain about.

It is in my math class. Even in classes for which I expect students to use calculators heavily, I expect them not to use calculators for basic computation. It's pointless to make students multiply two four-digit numbers by hand if they can already do it, or divide 3.51*10^5 by 4.3*10^(-9) manually if they can already do it, but if they can't already do it, they haven't achieved a basic level of math proficiency that we expect of high school graduates. And I certainly expect that my students will not reach for a calculator to multiply 17 by 5, or approximate pi/2, let alone the square root of 95.

Calculators are fabulous labor-saving tools. But a student who can't do arithmetic or basic algebra without one really does need remedial math. If her high school graduated her without these skills, it did her a disservice. But I don't think that means her college should just pass her along that way.

In your situation, I'd be annoyed and disappointed and frustrated, too. But I don't think the college is really the right entity for you to be ticked off at.

No one would ever mistake me for a math wiz and I used the same concept as BC. I knew that 9*9 =81 and 10*10 =100 since 100-95 =5, I would have also chosen the largest number over 9 and under 10.

My daughter also went to a school that did Marily Burns Math for smarty pants and knew how to do all sorts of abstract word problems but struggled doing basic arithmetic in her head. Yes, I whipped out my index cards and that is how she learned multiplication.

I agree with Garland about the over reliance on calculators. Kids with high tech calculators simply program formulas in their calculators and then plug and chug without really knowing how to do the work pen to the paper.

> think the college is really the right entity for you to be ticked off at.

Schools have 12 years to teach at least arithmetic and algebra. That is a very, very long time. If the schools aren't doing their jobs, then parents have to step in to fill the void. The problem is that parents often don't know that there is a problem.

I recall the survey results in grad school on how to improve courses. The biggest complaint was on students that didn't have the prerequisites for the course eating up valuable course time. How can a college professor teach the required material if a lot of course time is spent doing prerequisites?

In this case, the placement tests are fair to everyone. The professor can teach the course. Students in the course aren't held back by students that won't succeed in the course. Students that have to take remedial courses will be prepared for the course after they can demonstrate that they can meet the prerequisites.

At some level, the test should be designed to evaluate knowledge of the math concepts, not entirely the ability to perform arithmetic and estimation.

For example, I think it would be far more effective use of time to have several questions along the line of "What is ln(e^6.37)", rather than questions like "Estimate the number closest to e^6.37". In the case of the latter question, depending on the answer choices given, you would merely have to narrow it down and guess.